A228090 Numbers k for which a sum k + bitcount(k) cannot be obtained as a sum k2 + bitcount(k2) for any other k2<>k . Here bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

0, 1, 2, 5, 6, 7, 8, 9, 10, 13, 18, 21, 22, 23, 24, 25, 26, 30, 33, 37, 38, 39, 40, 41, 42, 45, 50, 53, 54, 55, 56, 57, 58, 61, 63, 64, 66, 69, 70, 71, 72, 73, 74, 77, 82, 85, 86, 87, 88, 89, 90, 94, 97, 101, 102, 103, 104, 105, 106, 109, 114, 117, 118, 119, 120

Offset

1,3

Comments

In other words, numbers k such that A228085(A092391(k)) = 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for Colombian or self numbers and related sequences

Example

0 is in this sequence because the sum 0+A000120(0)=0 cannot be obtained with any other value of k than k=0.
1 is in this sequence because the sum 1+A000120(1)=2 cannot be obtained with any other value of k than k=1.
2 is in this sequence because the sum 2+A000120(2)=3 cannot be obtained with any other value of k than k=2.
3 is not in this sequence because the sum 3+A000120(3)=5 can also be obtained with value k=4, as also 4+A000120(4)=5.

Prog

(Scheme, with Antti Karttunen's IntSeq-library) (define A228090 (MATCHING-POS 1 0 (lambda (k) (= 1 (A228085 (A092391 k))))))

Crossrefs

Sequence A228089 sorted into ascending order. Complement: A228236.

Cf. also A092391, A228085, A228088.

Sequence in context: A047581 A039067 A202114 * A287440 A111175 A047326

Adjacent sequences: A228087 A228088 A228089 * A228091 A228092 A228093

Keyword

nonn,base

Author

Antti Karttunen, Aug 17 2013

Status

approved